Delete/merge mutliple vertices on the same spot
Select every vertex with A, hit W and select remove doubles .
 you may have to adjust the merge distance if they are not exactly on the same spot.
  

To make vertices that are on the same location merge automatically, enable automerge.




Another option is to select all the vertices again with A then press Space to open the search, then type Remove doubles (Or for saving time, just "dou")

Then press enter or click on it.